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Derivation and analysis of simplified filters
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Lee, Wonjung and Stuart, A. M. (2017) Derivation and analysis of simplified filters. Communications in Mathematical Sciences, 15 (2). pp. 413-450. doi:10.4310/CMS.2017.v15.n2.a6
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Official URL: http://dx.doi.org/10.4310/CMS.2017.v15.n2.a6
Abstract
Filtering is concerned with the sequential estimation of the state, and uncertainties, of a Markovian system, given noisy observations. It is particularly difficult to achieve accurate filtering in complex dynamical systems, such as those arising in turbulence, in which effective low-dimensional representation of the desired probability distribution is challenging. Nonetheless recent advances have shown considerable success in filtering based on certain carefully chosen simplifications of the underlying system, which allow closed form filters. This leads to filtering algorithms with significant, but judiciously chosen, model error. The purpose of this article is to analyze the effectiveness of these simplified filters, and to suggest modifications of them which lead to improved filtering in certain time-scale regimes. We employ a Markov switching process for the true signal underlying the data, rather than working with a fully resolved DNS PDE model. Such Markov switching models haven been demonstrated to provide an excellent surrogate test-bed for the turbulent bursting phenomena which make filtering of complex physical models, such as those arising in atmospheric sciences, so challenging.
| Item Type: | Journal Article | ||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
| Library of Congress Subject Headings (LCSH): | Dynamics, Markov processes | ||||||||
| Journal or Publication Title: | Communications in Mathematical Sciences | ||||||||
| Publisher: | International Press | ||||||||
| ISSN: | 1539-6746 | ||||||||
| Official Date: | February 2017 | ||||||||
| Dates: |
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| Volume: | 15 | ||||||||
| Number: | 2 | ||||||||
| Page Range: | pp. 413-450 | ||||||||
| DOI: | 10.4310/CMS.2017.v15.n2.a6 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||
| Funder: | European Research Council (ERC), Engineering and Physical Sciences Research Council (EPSRC), Great Britain. Office for Nuclear Regulation (ONR) | ||||||||
| Grant number: | Grant No. 226488 (ERC) | ||||||||
| Adapted As: |
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